Thermochemical Properties and Bond Dissociation Enthalpies of 3- to

Article pubs.acs.org/JPCA

Thermochemical Properties and Bond Dissociation Enthalpies of 3to 5‑Member Ring Cyclic Ether Hydroperoxides, Alcohols, and Peroxy Radicals: Cyclic Ether Radical + 3O2 Reaction Thermochemistry Itsaso Auzmendi-Murua and Joseph W. Bozzelli* Department of Chemistry and Chemical Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102, United States S Supporting Information *

ABSTRACT: The formation of cyclic ethers is a major product in the oxidation of hydrocarbons, and the oxidation of biomass derived alcohols. Cyclic ethers are formed in the initial reactions of alkyl radicals with dioxygen in combustion and precombustion processes that occur at moderate temperatures. They represent a significant part of the oxygenated pollutants found in the exhaust gases of engines. Cyclic ethers can also be formed from atmospheric reactions of olefins. Additionally, cyclic ethers have been linked to the formation of the secondary organic aerosol (SOA) in the atmosphere. In combustion and thermal oxidation processes these cyclic ethers will form radicals that react with 3O2 to form peroxy radicals. Density functional theory and higher level ab initio calculations are used to calculate thermochemical properties and bond dissociation enthalpies of 3 to 5 member ring cyclic ethers (oxirane, yC2O, oxetane, yC3O, and oxolane, yC4O), corresponding hydroperoxides, alcohols, hydroperoxy alkyl, and alkyl radicals which are formed in these oxidation reaction systems. Trends in carbon−hydrogen bond dissociation energies for the ring and hydroperoxide group relative to ring size and to distance from the ether group are determined. Bond dissociation energies are calculated for use in understanding effects of the ether oxygen in the cyclic ethers, their stability, and kinetic properties. Geometries, vibration frequencies, and enthalpies of formation, ΔH°f,298, are calculated at the B3LYP/6-31G(d,p), B3LYP/6-31G(2d,2p), the composite CBS-QB3, and G3MP2B3 methods. Entropy and heat capacities, S°(T) and Cp°(T) (5 K ≤ T ≤ 5000), are determined using geometric parameters and frequencies from the B3LYP/6-31G(d,p) calculations. The strong effects of ring strain on the bond dissociation energies in these peroxy systems are also of fundamental interest. Oxetane and oxolane exhibit a significant stabilization, 10 kcal mol−1, lower ΔfH°298 when an oxygen group is on the ether carbon relative to the isomer with the oxygen group on a secondary carbon. Relative to alkane systems the ether oxygen decreases bond dissociation energies (BDEs) on carbon sites adjacent to the ether by ∼5 kcal mol−1, and increases BDEs on nonether carbons ∼1 kcal mol−1. The cyclic structures have significant effects on the C− H, CO−OH, COO−H, and CO−H bond dissociation enthalpies. These values can be used to help calibrate calculations of larger more complex bicyclic and tricyclic hydrocarbon and ether species.

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INTRODUCTION There is an increased need to improve the efficiency of the available combustion processes, and the necessity of developing alternative fuels, to reduce the emissions of CO2 and other pollutants. One new technique is the homogeneous charge compression ignition (HCCI) engine, which is considered as a promising engine for improved control of NOx and particulate emissions. In these engines, the autoignition process is strongly controlled by chemical kinetics of the peroxy radical chemistry. Accurate models to describe the chemistry behind the autoignition behavior of different fuels require accurate thermochemical properties of the reactant and intermediate species. Experimental studies by Baldwin, Walker, and coworkers1−4 in the 1980s and more recently by Dagaut and coworkers5−7 have shown that cyclic ethers are important, lowest barrier reaction products in the oxidation of linear and branched hydrocarbons. Recent studies have shown that the © 2014 American Chemical Society

formation of cyclic ethers is one of the main paths in the oxidation of hydrocarbons.8 One example of these reaction paths is illustrated in Figure 1 for the oxidation of isooctane. Biomass derived alcohol fuels such as ethanol,9,10 propanol,11−13 butanol,11,14−18 and pentanol19,20 have been investigated in theoretical and experimental studies, and all of these studies have also shown the formation of cyclic ethers. Figure 2 illustrates this for isopentanol. Cyclic ethers can also be formed from atmospheric reactions of olefins, following the steps: (i) •OH addition, (ii) O2 association, (iii) loss of NO2 by reaction with NO, and (iv) cyclization by O• addition to the secondary π bond, which forms the cyclic ether. A potential energy path diagram for the Received: December 24, 2013 Revised: March 22, 2014 Published: March 24, 2014 3147

dx.doi.org/10.1021/jp412590g | J. Phys. Chem. A 2014, 118, 3147−3167

The Journal of Physical Chemistry A

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Figure 1. Important initial reaction paths in oxidation of isooctane to form cyclic ethers.

Figure 2. Initial reaction paths in oxidation of isopentanol forming cyclic ethers.

formation of cyclic ethers from the oxidation of isoprene is illustrated in Figure 3. Cyclic ethers have also been linked to the formation of the secondary organic aerosol (SOA) in the atmosphere.21,22 Determination of thermochemical properties for these species is important for understanding the formation and the subsequent reactions of the cyclic ethers in combustion processes and in atmospheric chemistry. Further reactions include (i) a C−C bond cleavage that leads to the formation of a diradical, which subsequently can undergo unimolecular decomposition reactions, or react with a molecular oxygen, 3O2, to form a peroxy diradical,23 and (ii) loss of a hydrogen atom by abstraction, which leads to the formation of a cyclic alkyl radical. These alkyl radicals will further react by unimolecular

decomposition reactions (beta scission) or association with molecular oxygen, 3O2, to form a peroxy radical, which is illustrated in Figure 4. There are a number of studies on the thermochemistry of cyclic ethers;16−25 but there are fewer with thermochemistry of the radicals, the bond dissociation energies, and the peroxy radical systems. Our group has derived the thermochemical properties and studied the C−H bond dissociation energy trends versus ring size for cyclic alkanes, cyclic alkane peroxides, and methyl substituted cyclic ethers.24,25 We also studied the reactions derived from the ring-opening of cyclic alkanes and ethers,23 and several reaction mechanisms already include the decomposition reactions of the cyclic ethers.26,27 Ruzsinszky et al., with the aim of improving the rapid estimation of basis set 3148



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Figure 3. Oxidation of isoprene leading to formation of cyclic ethers. Units: kcal mol−1.

Figure 4. Decomposition pathways for cyclic ethers.

Scheme 1. Nomenclature and Figures of the yC2O Cyclic Ethers (y = cyclic; q = OOH)

oxolane are 93.1 kcal mol−1 leading to the α-furanyl and 97.9 kcal mol−1 leading to β-furanyl moieties. To the best of our knowledge, there is no available literature data for the thermochemical properties and the C−H, O−H, and O−OH bond dissociation energies of the cyclic ether hydroperoxides, peroxy radicals, and alkyl radicals. The goal of the present work is to develop the thermochemistry of peroxy and hydroperoxy-alkyl radicals formed by the cyclic ether radical plus 3O2 reactions (yC•2O-yC•4O + 3O2, y represents cyclic) using computational chemistry. One other objective of this study and a previous publication on these 3- to 5-member ring ethers and hydrocarbons is for

error and correlation energy from partial charges method (REBECEP), calculated the heats of formation of several oxygenated hydrocarbons, including oxirane and oxolane (−12.6 and −44.0 kcal mol−1, respectively).28 Wijaya et al. published data on the thermochemical properties of cyclic ethers at the BH&HLYP level of theory (−12.61, −19.65, and −44.58 kcal mol−1, respectively, for oxirane, oxetane, and oxolane).29 Bozzelli et al.30 also published data on oxetane (−19.24 kcal mol−1) at the B3LYP/6-31G(d,p) level of theory with the use of isodesmic work reactions. Agapito et al.31 studied bond dissociation enthalpies on oxolane at the CBS-Q level. Their calculated C−H bond dissociation enthalpies of 3149



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use in calculating thermochemical properties for larger bicyclic and tricyclic hydrocarbon and ether species with similar ring

strains. Comparison of the data using different density functional theory and ab initio methods and comparisons of 3150



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our theoretical results to the limited available experimental data are presented. Hudzik et al. have shown that use of single rings of similar size to intramolecular rings in bicyclics can be used to cancel errors for ring strain in density functional calculations.32 Schemes 1−3 illustrate the cyclic ether structures studied, along with the nomenclature used for each of the species. Here “y” stands for cyclic, “q” for OOH group, and “qj” for a peroxy radical ROO•. The nomenclature used for the position identification of the peroxy groups is as follows: (i) qeth (or qeth•) represents a hydroperoxide group (or peroxy radical group) bonded to a carbon in the ring adjacent to the ether oxygen. (ii) qsec (or qsec•) represents a hydroperoxide group (or peroxy radical group) bonded to a carbon in the ring that is NOT adjacent to an ether oxygen.

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CH3CH 2OCH•CH3 + O2 → CH3CH 2OCH(OO•)CH3 → CH3CH•OCH(OOH)CH3

CH3CH•OCH(OOH)CH3 + O2 → CH3CH(OO•)OCH(OOH)CH3 → [CH3CH(OOH)OC•(OOH)CH3 ]* [CH3CH(OOH)OC•(OOH)CH3 ]* → CH3CH(OOH)OC(O)CH3 + OH

The CH3CH(OOH)OC(O)CH3 has approximately up to 50 kcal mol−1 activation energy from the transition state, and this energy is sufficient to dissociate the RCO−OH bond on the remaining CO−OH hydroperoxide group. Depending on temperature and pressure conditions, some of the CH3CH(OOH)OC(O)CH3 will dissociate further to CH3CH(O•)OC(O)CH3 + OH. If this occurs in ethers as it does in ketones as Crounse indicates, the overall reaction is chain branching. In a different study, Pye et al.34 showed that prediction of aerosol formation from isoprene is strongly dependent on methyl tetrols and methyl glyceric acid which are resulting products of epoxide formation and subsequent conversion of epoxides to aerosols. The data of Pye et al. suggest that understanding the thermochemistry of organic epoxides and oxygenated epoxides will be of value in improving the aerosol formation rates and possibly bringing into agreement with experimental data. Data presented in this study illustrate the stabilizing effects of radicals on carbon atom adjacent to the ether site by the ether-oxygen result in significantly lower 4 −5 kcal mol−1 bond dissociation energies than on alkane systems and on nonether carbons. This reduced bond dissociation energy results in a facile abstraction of a hydrogen from the ether carbons.

IMPORTANT REACTIONS OF ETHERS IN ATMOSPHERIC AND COMBUSTION ENVIRONMENTS

Crounse et al.33 showed that the atmospheric oxidation of 3pentanone proceeds via a set of consecutive reactions starting with the radical site formation via OH radical abstraction, where the H atom is formed from a resonantly stabilized C−H bond adjacent to the carbonyl group. The C−H bond dissociation energy is lower than a conventional secondary bond by 5 kcal mol−1 due to the resonance of the carbon radical site with the carbonyl group. This carbon radical adjacent to a carbonyl group undergoes association reaction with 3O2, to form a peroxy radical with a well depth of approximately 10 kcal mol−1 deeper than a resonantly stabilized allyl radical. The peroxy radical then abstracts the similarly weakly bound hydrogen atom from the corresponding secondary carbon just across the carbonyl to form a hydroperoxide and a new resonance stabilized alkyl radical. 3O2 then adds to this new carbon radical site forming a RC(OOH)CO(COO•)R′ hydroperoxide−peroxy radical. The new peroxy radical undergoes an identical H atom abstraction from the hydroperoxide carbon; this forms a radical site on a carbon with a hydroperoxde group. This hydroperoxide carbon radical is not stable; it immediately undergoes electron rearrangement forming a RCO Π bond (a carbonyl) and cleaving the weak (∼45 kcal mol−1 RO−OH). This last step is ∼35 kcal mol−1 exothermic as the newly formed Π bond contributes approximately 80 kcal mol−1 of new energy. Crounse et al. showed that this process is dominant over other processes in the 3-pentanone oxidation. They also state that it will be important in the atmospheric oxidation of systems that form similar ketones, such as isoprene. Our data shows that this decrease in C−H bond dissociation energy is also present in cyclic ethers. Moreover, our work shows that the significant exothermicity of the ether carbon radical + 3O2 association reactions is similar to that of the ketones of the Crounse et al. data. The carbonyl study further compares the isomerization rates of the carbonyl in ketones with those of comparable structures in alkanes. They show the significant amplification in kinetics with the ketones. Our study illustrates that the same favorable conditions apply in cyclic ethers, and we suggest that ether oxidation in the atmosphere will also undergo this reaction set. Example:

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COMPUTATIONAL METHODS Electronic structural parameters, vibration frequencies, zeropoint vibrational and thermal energies, and internal rotor potentials for this set of compounds were calculated using the density functional theory B3LYP, and the composite methods CBS-QB3 and G3MP2B3. Isodesmic work reactions were used to calculate the heats of formation and bond dissociation enthalpies at all levels of theory. The B3LYP method combines the three parameter Becke exchange functional, B3, with Lee− Yang−Parr correlation functional, LYP.35 For the B3LYP method, the 6-31G(d,p) and the larger 6-31G(2d,2p) basis set were used. The two higher level composite, ab initio methods CBS-CB336 and G3MP2B3,37,38 which are based on B3LYP functional geometries and frequencies, were also used in the work reaction calculations. CBS-QB3 is a multilevel model chemistry that predicts molecular energies with high accuracy and relatively low computational cost. It combines the results of several ab initio and DFT individual methods and empirical correction terms to predict molecular energies with high accuracy and relatively low computational cost. It is based on B3LYP/CBSB7 calculations for the geometry optimization and frequencies, followed by a single point energy calculation at the CCSD(T)/6-31g+(d′) and MP4SDQ/CBSB4 level of theory. It includes a total energy extrapolation to the infinite 3151



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Table 1. Standard Enthalpies of Formation at 298.15 K of Reference Speciesa

a

species

ΔH°f,298

ref

species

ΔH°f,298

ref

y(CH2CH2CH2) y(CH2CH•CH2) y(CH2CH2CH2CH2) y(CH2CH•CH2CH2) y(CH2CH2CH2CH2CH2) y(CH2CH•CH2CH2CH2) y(CH2CH2CH)OOH y(CH2CH2CH2CH)OOH y(CH2CH2CH2CH2CH)OOH y(CH2CH2CH)OO• y(CH2CHCH2CH)OO•

12.74 ± 0.12 69.74 6.62 ± 0.26 54.88 −18.26 ± 0.19 26.09 −7.54 −17.36 −42.21 27.41 16.01

58 24 58 24 58 24 24 24 24 24 24

y(CH2CH2CH2CH2CH)OO• y(CH•CH2CH)OOH y(CH2CH•CH)OOH y(CH•CHCH2CH)OOH y(CH2CH•CH2CH)OOH y(CH•CH2CH2CH2CH)OOH y(CH2CH•CH2CH2CH)OOH CH3CH2CH2CH3 CH3OCH3 CH3CH2OCH3 CH3CH2CH3

−8.99 50.11 45.26 31.79 31.32 3.74 3.29 −35.08 ± 0.14 −43.99 −51.73 −25.02 ± 0.12

24 24 24 24 24 24 24 59 60 60 59

Units: kcal mol−1.

Δrxn H °298 = ΣΔHf products − ΣΔHf reactants

basis-set limit using pair natural-orbital energies at the MP2/ CBSB3 level, and an additive correction at the CCSD(T) level of theory. The modified Gaussian-3 (G3) theory referred as G3MP2B3 (G3MP2//B3LYP/6-31g(d)) uses geometries and ZPVE scaled by 0.96 from B3LYP/6-31g(d) calculations. All quantum chemical calculations were performed within the Gaussian-03 software package.39 Rotational conformers related to the peroxide group (R− OOH and RO−OH rotors) were studied to determine the lowest energy conformer of each parent and radical. The resulting internal rotor potentials were also used for calculation of entropy and heat capacity contributions. The Supporting Information summarizes the geometries for each of the molecules studied. The potential energies for internal rotor potentials were computed at the B3LYP/6-31G(d,p) level of theory, by scanning each dihedral angle between 0° and 360° in steps of 10°, while all remaining coordinates were fully optimized. All dihedrals were rescanned when a lower energy conformer was identified, relative to the initial low energy structure, in order to ensure the lowest energy conformer was calculated. The total energy corresponding to the most stable conformer was set to zero and used as a reference point in the plots of the potential barriers. Appendix A in the Supporting Information contains the figures for the rotational analysis performed for each of the species studied, as well as the resulting potential energy barriers for internal rotations in the stable nonradical and radical molecules. Enthalpies of formation (ΔfH°298) were evaluated using calculated energies, zero point vibration energy (ZPVE), plus thermal contributions (to 298 K) at the B3LYP/6-31G(d,p), B3LYP/6-31G(2d,2p), CBS-QB3, and G3MP2B3 levels of theory plus use of work reactions.40,41 The calculated total energy at B3LYP/6-31G(d,p) is corrected by the ZPVE, which is scaled by 0.9806, as recommended by Scott and Radom.42 The G3MP2B337,38 uses geometries from B3LYP/6-31g(d) calculations. Isodesmic work reactions with group balance were used to improve accuracy in calculation of enthalpy of formation values. Isodesmic reactions conserve the number of types of bonds, and reaction schemes with similar bonding on both sides of the reaction provide a cancellation of systematic errors that arises in quantum chemical calculations due to the incomplete capture of the electron correlation energy.43,44 We used the calculated ΔrxnH298 of each work reaction to calculate the ΔfH°298 of the target reactant:

where the two products and one reactant are the reference molecules that have known, evaluated ΔfH°(298) from literature. Entropy and heat capacity values as a function of temperature were determined from the calculated structures, moments of inertia, vibration frequencies, internal rotor potentials, symmetry, electron degeneracy, number of optical isomers, and the known mass of each molecule. The calculations used standard formulas from statistical mechanics for the contributions of translation, vibrations, and external rotation (TVR) using the SMCPS (Statistical Mechanics−Heat Capacity, Cp, and Entropy, S) program.45 This program utilizes the rigidrotor-harmonic oscillator approximation from the frequencies along with moments of inertia from the optimized B3LYP/631G(d,p) level. Lower frequency vibrational modes that resemble torsions around single bonds were treated as hindered internal rotors, instead of treating them as torsion frequencies. Energy profiles for internal rotations were calculated to determine energies of the rotational conformers and interconversion barriers along with contributions to entropy and heat capacity for the low barrier rotors. In this study, all internal rotors studied, hydroperoxides (Y−OOH) and (Y−O−OH), were treated as hindered rotors, rather than as harmonic oscillators. The contributions to entropy and heat capacity of these internal rotors were calculated using ROTATOR,46 which also accounts directly for contributions to entropy from the optical isomers. Coupling of the low barrier internal rotors with vibrations was not included. For hindered rotors, a relaxed rotational scan was done with dihedral angle increments of 10° using B3LYP/6-31G(d,p) and the potential obtained was fitted to a truncated Fourier series expansion of the form: 10

V (θ ) = a 0 +

10

∑ an cos(nθ) + ∑ bn sin(nθ) n=1

n=1

m

a0 =

∑i = 1 fi

bn =

(1)

m

an =

;

m m ∑i = 1 fi sin(nθ ) m

∑i = 1 fi cos(nθ) m

;

(2)

The program ROTATOR uses the potential to solve the 1-D Schrödinger equation in θ to calculate the energy levels and, therefore, the partition function of the hindered rotor. The program calculates the Hamiltonian matrix in the basis of the 3152



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Table 2. Standard Enthalpies of Formation at 298.15 K of Alcohols and Alkoxy Radicals Calculated in this Studya

a

species

ΔH°f,298

species

ΔH°f,298

y(CH2CH2CH)OH y(CH2CH2CH2CH)OH y(CH2CH2CH2CH2CH)OH y(CH2CHO)OHeth y(CH2CH2CHO)OHeth y(CH2CH2CHO)OHsec y(CH2CH2CH2CHO)OHeth y(CH2CH2CH2CHO)OHsec

−24.64 −34.50 −58.91 −59.23 −67.13 −57.43 −92.52 −81.75

y(CH2CH2CH)O• y(CH2CH2CH2CH)O• y(CH2CH2CH2CH2CH)O• y(CH2CHO)O•eth y(CH2CH2CHO)O•eth y(CH2CH2CHO)O•sec y(CH2CH2CH2CHO)O•eth y(CH2CH2CH2CHO)O•sec

16.07 17.63 −5.95 −11.26 −14.90 −4.49 −36.59 −27.32


Table 3. Calculated Enthalpies of Formation at 298 K of Oxirane and Its Derivativesa ΔH°f,298 B3LYP species y(cco) σ y(cco)qeth y(c•co)

y(cco)qeth•

y(c•co)qeth

y(cc•o)qeth

σ BDE σ BDE σ BDE σ

6-31G(d,p)

6-31G(2d,2p)

CBSQB3

G3MP2B3

avg DFT

avg composite

avg methods

−12.35 0.57 −40.48 1.04 39.40 104.22 0.55 −0.57 90.61 0.12 12.66 103.84 0.36 15.06 106.2 0.13

−12.01 0.44 −40.31 1.01 39.39 104.21 0.58 −0.81 90.37 0.18 12.49 103.67 0.38 14.97 106.2 0.03

−12.63 0.32 −39.04 0.02 39.88 104.70 0.06 −0.71 90.47 0.23 13.31 104.49 0.32 15.97 107.2 0.26

−12.80 0.29 −39.12 0.02 39.49 104.31 0.06 −0.82 90.36 0.22 12.99 104.17 0.24 15.87 107.1 0.20

−12.18 0.24 −40.39 0.11 39.39 104.21 0.00 −0.69 90.49 0.17 12.57 103.75 0.12 15.02 106.2 0.06

−12.72 0.12 −39.08 0.06 39.69 104.51 0.28 −0.77 90.41 0.08 13.15 104.33 0.23 15.92 107.1 0.07

−12.45 0.35 −39.74 0.76 39.54 104.36 0.23 −0.73 90.45 0.11 12.96 104.04 0.36 15.47 106.7 0.52

literature −12.58,61 −12.6,28 −12.61,62 −13.2029

35.8 ± 1.547 100.5 ± 1.547

a Units: kcal mol−1. *Standard deviation (σ) does not include the uncertainties of the reference species. BDE = bond dissociation enthalpy. avg DFT = Average between 6 and 31G(d,p) and 6-31G(2d,2p). avg composite = average between CBS-QB3 and G3MP2B3.

study. The Supporting Information summarizes the heats of formation obtained from each of the work reactions, for all methods. The standard enthalpies of formation calculated are shown in Tables 3−5. The calculated standard enthalpies of formation for oxirane, oxetane, and oxolane parent ethers are −12.72, −19.16, and −43.97 kcal mol−1, respectively. These all show agreement, within ∼0.5 kcal mol−1, with reported literature data as shown in Table 3. The thermochemistry chemistry of these three cyclic ethers, their alcohols and peroxides, and corresponding radicals, corresponding to loss of a hydrogen atom, is found to vary significantly with the two types of carbon sites in these three cyclics. Oxirane has two carbons and each are bonded to the ether group, termed ether carbons (Cet). Oxitane and oxolane have two types of carbons, ether carbons (Cet) and secondary carbons (Csec), where the secondary carbons are not bonded to an ether oxygen. Enthalpies of formation for oxirane hydroperoxide and oxirane alcohol are −39.08 and −59.23 kcal mol−1, respectively, where in oxirane the hydroperoxide and hydroxyl groups are restricted by structure and only bonded to ether carbons. Oxitane is a 4-member ring ether with two ether carbons and one secondary carbon. Standard enthalpy values for oxitane hydroperoxide are −51.11 and −39.94 kcal mol−1 for the

wave function of free internal rotation and performs the subsequent calculation of energy levels by diagonalization of the Hamiltonian matrix. From the obtained partition functions, the contribution to entropy and heat capacity are determined according to standard expressions of statistical thermodynamics. Entropy and heat capacity values obtained from SMCPS and ROTATOR are summed and used to calculate the entropy and heat capacity of the calculated species versus temperature.

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RESULTS AND DISCUSSION Enthalpies of Formation. Enthalpies of formation (ΔfH°298) were evaluated using calculated energies, zero point vibration energy (ZPVE), plus thermal contributions (to 298 K) at the B3LYP/6-31G(d,p), B3LYP/6-31G(2d,2p), CBS-QB3, and G3MP2B3 levels of theory plus use of work reactions. The standard enthalpies of formation at 298.15 K of the reference species used in the reactions are summarized in Tables 1 and 2. Table 2 includes the heats of formation of the cyclic ether alcohols and the respective alkoxy radicals calculated in this work at the B3LYP/6-31G(d,p) and CBSQB3 levels of theory in conjunction with isodesmic work reactions. Appendix B in the Supporting Information contains an example of the use of work reactions, as well as some example work reactions used for the determination of the enthalpy of formation of all the species determined in this 3153



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Table 4. Calculated Enthalpies of Formation at 298 K of Oxetane and Its Derivativesa ΔH°f,298 B3LYP species y(ccco) σ y(ccco)qeth σ y(ccco)qsec y(c•cco)

y(cc•co)

y(ccco)qeth•

y(c•cco)qeth

y(cc•co)qeth

y(ccco)qsec•

y(c•cco)qsec

σ BDE σ BDE σ BDE σ BDE σ BDE σ BDE σ BDE σ

6-31G(d,p)

6-31G(2d,2p)

CBS-QB3

G3MP2B3

avg DFT

avg composite

avg methods

−19.77 0.57 −51.60 1.04 −40.47 1.04 24.65 95.49 0.55 31.01 101.85 0.55 −12.59 90.62 0.42 −4.66 98.55 0.12 1.11 104.32 0.34 −5.06 86.98 0.22 2.23 94.27 0.10

−18.83 0.44 −51.55 1.01 −40.49 1.01 24.60 95.44 0.58 31.10 101.94 0.58 −12.65 90.56 0.41 −4.81 98.40 0.09 1.21 104.42 0.36 −5.17 86.87 0.20 2.20 94.24 0.10

−19.46 0.32 −51.10 0.02 −39.90 0.02 24.56 95.40 0.06 30.80 101.64 0.06 −13.21 90.00 0.36 −4.88 98.33 0.09 0.60 103.81 0.30 −5.43 86.61 0.19 2.38 94.42 0.08

−18.86 0.29 −51.12 0.02 −39.97 0.02 24.62 95.46 0.06 30.93 101.77 0.06 −13.44 89.77 0.37 −4.93 98.28 0.09 0.55 103.76 0.29 −5.53 86.51 0.19 2.38 94.42 0.08

−19.30 0.07 −51.58 0.04 −40.48 0.01 24.63 95.47 0.03 31.05 101.89 0.06 −12.62 90.59 0.04 −4.73 98.48 0.10 1.16 104.37 0.07 −5.12 86.92 0.07 2.21 94.25 0.02

−19.16 0.18 −51.11 0.02 −39.94 0.05 24.59 95.43 0.04 30.87 101.71 0.09 −13.32 89.89 0.16 −4.91 98.30 0.04 0.57 103.78 0.04 −5.48 86.56 0.07 2.38 94.42 0.00

−19.23 0.13 −51.34 0.27 −40.21 0.31 24.61 95.45 0.04 30.96 101.80 0.13 −12.97 90.24 0.42 −4.82 98.39 0.12 0.87 104.08 0.34 −5.30 86.74 0.22 2.30 94.34 0.10

literature −19.25,63 −19.24,30 −19.6529

Units: kcal mol−1. *Standard deviation (σ) does not include the uncertainties of the reference species. BDE = bond dissociation enthalpy. avg DFT = Average between 6 and 31G(d,p) and 6-31G(2d,2p). avg composite = Average between CBS-QB3 and G3MP2B3. a

H bond on propane. The oxirane C−H bond follows the dimethyl ether trend. The available literature data for the ΔfH°298 of oxirane radical47 is 35.8, which corresponds to a bond dissociation energy of 100.5; these literature values are 4 kcal mol−1 lower than the values calculated in this study. Oxitane has Cet and Csec sites, and the standard enthalpy values for the respective radicals are 24.6 and 30.9 kcal mol−1 with corresponding BDEs of 95.4 and 101.7 kcal mol−1 (see Table 4). Oxolane has Cet and Csec sites, and the standard enthalpy values for the respective radicals are −2.0 and 2.5 kcal mol−1 with corresponding BDEs of 93.7 and 98.3 kcal mol−1 (see Table 5). Luo47 reports a C−H bond dissociation energy for oxolane of 92.1 and enthalpy of formation for oxolane radical of −4.3 kcal mol−1, which is 2.3 kcal mol−1 lower than the value in the present work. A C−H bond dissociation energy of 93.1 was reported by Agapito et al.,31 which is 0.6 kcal mol−1 lower than the Cet BDE of this study. The calculated standard enthalpies of formation for oxirane, oxetane and oxolane peroxy radicals are −0.77, −13.32/−5.48 (qeth/q sec ), and −39.10/−32.34 (q eth/q sec ) kcal mol −1 , respectively. Enthalpies of formation for oxirane hydroperoxide radical are 13.15 and 15.92 kcal mol−1 for the radical site on the ether carbon and on the hydroperoxide carbon, respectively.

hydroperoxy group bonded to ether carbon, y(ccco)qet, and bonded to a secondary carbon, y(ccco)qsec, respectively. There is a significant (11.2 kcal mol−1) stabilization resulting from interaction of the peroxy group and the ether oxygen link. Ether carbon versus secondary carbon trends in enthalpy of formation for oxitane alcohols are similar, −67.13 and −57.43 kcal mol−1, respectively, where the hydroxyl group is bonded to ether carbon, y(ccco)ohet, and bonded to a secondary carbon, y(ccco)ohsec, respectively. Enthalpy of formation for oxolane peroxides shows similar stabilization for the peroxide on the ether carbon, ΔfH°298 at −75.63 and −66.50 kcal mol−1 for y(cccco)qet and y(cccco)qsec, respectively. Enthalpies of formation for oxitane alcohol are −92.52 and −81.75 kcal mol−1, respectively, where the hydroxyl groups bonded to ether carbon, y(cccco)ohet, and bonded to a secondary carbon, y(cccco)ohsec, respectively. While there is an overall difference in the alcohol and hydroperoxide cyclic ether Cet and Csec hydroperoxide formation enthapies of ∼10 kcal mol−1, there is only a ∼5 kcal mol−1 difference in the enthalpy of formation for the Cet versus the Csec radicals, and in the Cet−H and Csec−H bond dissociation energies (see discussion below). The calculated ΔfH°298 for the oxirane radical (yc•co) is 39.7 kcal mol−1 with a Cet−H radical corresponding bond dissociation energy of 104.51. The C−H bond dissociation energy on cyclopropane is 109 kcal mol−1 and the C−H bond on dimethyl ether is ∼6 kcal mol−1 lower than the primary C− 3154



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Table 5. Calculated Enthalpies of Formation at 298 K of Oxolane and Its Derivativesa ΔH°f,298 B3LYP species y(cccco) σ y(cccco)qeth σ y(cccco)qsec y(c•ccco)

y(cc•cco)

y(cccco)qeth•

y(c•ccco)qeth

y(cc•cco)qeth

y(ccc•co)qeth

y(cccco)qsec•

y(c•ccco)qsec

y(ccc•co)qsec

y(cccc•o)qsec

σ BDE σ BDE σ BDE σ BDE σ BDE σ BDE σ BDE σ BDE σ BDE σ BDE σ

6-31G(d,p)

6-31G(2d,2p)

CBS-QB3

G3MP2B3

avg DFT

avg composite

avg methods

−44.51 0.57 −75.60 1.04 −66.07 1.04 −2.18 93.58 0.55 2.50 98.26 0.55 −38.65 89.08 0.22 −31.09 96.64 0.27 −28.67 99.06 0.02 −27.88 99.85 0.07 −32.24 86.36 0.06 −26.66 91.94 0.30 −18.84 99.76 0.14 −24.22 94.38 0.25

−43.93 0.44 −75.20 1.01 −65.81 1.01 −1.99 93.77 0.58 2.72 98.48 0.58 −38.84 88.89 0.19 −31.28 96.45 0.29 −28.66 99.07 0.02 −27.74 99.99 0.06 −32.24 86.36 0.06 −26.55 92.05 0.28 −18.78 99.82 0.13 −24.30 94.30 0.27

−44.30 0.32 −75.65 0.02 −66.49 0.02 −2.01 93.75 0.06 2.47 98.23 0.06 −39.05 88.68 0.18 −30.70 97.03 0.23 −28.62 99.11 0.01 −27.88 99.85 0.03 −32.32 86.28 0.05 −26.20 92.40 0.26 −18.59 100.01 0.12 −23.81 94.79 0.22

−43.63 0.29 −75.62 0.02 −66.52 0.02 −2.02 93.74 0.06 2.55 98.31 0.06 −39.16 88.57 0.18 −30.78 96.95 0.20 −28.64 99.09 0.01 −27.87 99.86 0.03 −32.36 86.24 0.05 −26.01 92.59 0.27 −18.54 100.06 0.12 −23.83 94.77 0.21

−44.22 0.08 −75.40 0.28 −65.94 0.18 −2.08 96.68 0.14 2.61 98.37 0.16 −38.75 88.98 0.13 −31.19 96.54 0.13 −28.67 99.06 0.01 −27.81 99.92 0.09 −32.24 86.36 0.00 −26.61 91.99 0.08 −18.81 99.79 0.04 −24.26 94.34 0.06

−43.97 0.03 −75.63 0.02 −66.50 0.02 −2.02 93.74 0.01 2.51 98.27 0.06 −39.10 88.63 0.08 −30.74 96.99 0.06 −28.63 99.10 0.02 −27.88 99.85 0.01 −32.34 86.26 0.03 −26.11 92.49 0.13 −18.57 100.03 0.03 −23.82 94.78 0.02

−44.09 0.06 −75.52 0.21 −66.22 0.34 −2.05 93.71 0.09 2.56 98.32 0.11 −38.93 88.80 0.22 −30.96 96.77 0.27 −28.65 99.08 0.02 −27.84 99.89 0.07 −32.29 86.31 0.06 −26.36 92.24 0.30 −18.69 99.91 0.14 −24.04 94.56 0.25

literature −44.03,64 −44.0,28 −44.5829

−4.3 ± 1.547 93.1,31 92.1 ± 1.647

97.931

a Units: kcal mol−1. *Standard deviation (σ) does not include the uncertainties of the reference species. BDE = bond dissociation enthalpy. avg DFT = Average between 6 and 31G(d,p) and 6-31G(2d,2p). avg composite = average between CBS-QB3 and G3MP2B3

Enthalpies of formation and bond dissociation energies are usually not reported for peroxide or hydroperoxide carbon sites as the radicals typically dissociate without a barrier and the reaction is strongly exothermic. Kuwata et al. have shown the reaction proceeds without a barrier48 for ketone and aldehydic alkyl systems. The peroxy radicals are formed by association of a hydrocarbon radical with 3O2, and there is not an initial, stable hydroperoxide moiety. We note that in combustion chemistry hydroperoxide alkyl radicals can be formed via intramolecular H atom transfer; but these transfer reactions have barriers and usually do not occur in atmospheric chemistry. Zhu et al.49 report that the C−H bonds on carbon sites of normal alkylperoxides are ∼3−5 kcal mol−1 weaker than the C−H bonds on corresponding nonperoxide carbon sites, from analysis of abstraction barriers. In calculations on the oxirane system, we did find a minimum energy for the radical on the peroxide carbon. The enthalpy of formation for this strained cyclic, oxirane alkyl hydroperoxide

Standard enthalpy values for oxitane hydroperoxide carbon radicals with the hydroperoxide group bonded to the ether carbon are −4.91 y(c•ccco)qet and 0.57 kcal mol−1 y(ccjcco)qet for the radical site on the ether carbon and on the secondary carbon, respectively. The oxitane hydroperoxide carbon (y(c•cco)qsec) radical with the hydroperoxide group bonded to the secondary carbon is 2.38 kcal mol−1, here the radical site is on an ether carbon. Calculated enthalpy of formation values for oxolane hydroperoxide radicals with the hydroperoxide group bonded to the ether carbon are −30.74, −28.63, and −27.88 kcal mol−1 for the radical site on the ether carbon and on the secondary carbon, respectively. The enthalpies for the oxolane hydroperoxide radical with the hydroperoxide group bonded to the secondary carbon are −26.11, −23.82, and −18.57 kcal mol−1 for the radical site on the ether carbon and on the secondary carbon, respectively. 3155



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Table 6. Calculated Uncertainties for Each Methoda B3LYP/6-31G(d,p)

B3LYP/6-31G(2d,2p)

CBS-QB3

G3MP2B3

2.07 0.75 ±1.56 ±2.82

2.04 0.75 ±1.54 ±2.79

0.12 0.75 ±0.54 ±0.87

0.12 0.75 ±0.54 ±0.87

uncertainty from method uncertainty from reference species RMS simple sum two uncertainities a


Table 7. Summary of Recommended Valuesa

a


in Figures 11−13 will involve bicyclic structures. It is therefore important to evaluate the H atom transfer reactions to the peroxy radical oxygen sites from the ipso carbon (peroxy bonded carbon) in analysis for important kinetics. As noted above, these radicals will rapidly further react to the corresponding lactone and OH radical. The enthalpy of formation data for the three cyclic ethers show good agreement between the density functional theory (B3LYP) and higher level composite methods (CBS-QB3 and G3MP2B3). The higher level composite methods present a higher consistency between the values obtained, and the average value of the CBS-QB3 and G3MP2B3 calculations (indicated in bold in the tables) is recommended. We report the DFT data to support the use of work reactions as the results suggest they can help cancel systematic calculation error.

with the radical site in the peroxide carbon, is estimated as 2.77 kcal mol−1 higher (ΔH°f,298 of 15.9 kcal mol−1) than the heat of formation of the oxirane alkyl hydroperoxide with the radical site in the non peroxide carbon (ΔH°f,298 =13.15 kcal mol−1). This y(COC•)OOH radical intermediate is not stable, as dissociation to y(COC(O)) + OH is exothermic; it requires electron and some small structure rearrangement to cleave the very weak RO−OH bond and form the π bond of a carbonyl plus •OH. It has been shown that cyclic ether ketone (lactone) plus •OH radical (acetolactone, ΔH°f,298 = −47.3 kcal mol−1)33 are formed and reported to have no barrier.50 Propiolactone, ΔH°f,298 = −68.4 kcal mol−1, is formed from this oxidation of oxetane,34 and butyrolactone, ΔH°f,298 = −87.0 kcal mol−1, is formed from the oxidation of oxolane.2 The cyclic ethers in this study all have strain, and the transition states for the hydrogen transfer reactions illustrated 3156



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Table 8. Comparison of Secondary C−H bond Dissociation Enthalpies for yC2O-yC4O Cyclic Ethersd

a

Reference 24. bReference 51. cReference 52. dUnits: kcal mol−1.

enthalpies of parent molecule and product species are calculated in this study in conjunction with the value of 52.10 kcal mol−1 for the hydrogen atom at 298.15 K. Table 8 provides a comparison of the secondary C−H bond dissociation enthalpies for cyclic alkanes and ethers, at different positions of the rings. Table 8 lists C−H bond dissociation enthalpies for the several different carbon ring sites. (i) Group 1 (Cjsec): Cyclic ether, radical site on secondary (nonether) carbon, separated from the ether oxygen by one or more carbons. (ii) Group 2 (Cjeth): Cyclic ether, radical site on ether carbon. (iii) Group 3 (Cjsec-QCeth): Cyclic ether peroxide, radical site is on secondary carbon, peroxy group is on the ether carbon. (iv) Group 4 (Cjeth-QCeth): Cyclic ether peroxide, radical site is on ether carbon, peroxy group is on an ether carbon. (v) Group 5 (Cjsec-QCsec): Cyclic ether peroxide, radical site is on secondary carbon, peroxy group is on secondary carbon. (vi) Group 6 (Cjeth-QCsec): Cyclic ether peroxide, radical site is on ether carbon, peroxy group is on secondary carbon. Figure 5 compares the results obtained for the C−H bond dissociation enthalpies on these cyclic ethers and cyclic ether hydroperoxides. Enthalpies of formation and bond dissociation energies for radical sites on nonether carbon sites (group 1) are 4.6 and 6.3 kcal mol−1 higher (for oxetane and oxolane, respectively) versus ether carbon sites (group 2). The trend is similar to that observed between linear alkanes and ethers, where the C−H bond dissociation enthalpies are ∼4 kcal mol−1 higher on a corresponding non ether carbon. C−H bond dissociation enthalpies on cyclic ethers on nonether carbon sites (group 1) are 1.3−1.8 kcal mol−1 higher than the C−H

Table 6 represents the uncertainties calculated for each of the methods used, accounting for the uncertainty from the work reactions, and the uncertainty of the reference species used in the respective work reactions and assuming the work reactions cancel the systematic error. Appendix C in the Supporting Information contains an explanation of the calculation method for the uncertainties. Table 7 represents a summary of the heats of formation (ΔH°f,298) and bond dissociation enthalpies (BDEs) recommended for each of the systems studied. Bond Dissociation Enthalpies. The C−H bond dissociation enthalpies are important fundamental properties that reflect the corresponding radical’s stability in atmospheric and combustion reaction systems. Bond dissociation energies (BDEs) serve to identify carbon sites where C−H bond cleavage will occur in abstraction of H atoms from the carbons and in elimination (beta scission) reactions. R−OO bonds reflect the chemical activation energy in the alkyl radical plus 3 O2 association reactions. RO−OH bonds are typically the weakest bond in a normal hydroperoxide system at about 45 kcal mol−1 and reflect the low stability of hydroperoxides. ROO−H bond dissociation energies reflect loss or gain of a moderately weak hydrogen−oxygen σ bond and are important in evaluation of intramolecular hydrogen transfer reaction. C−H Bond Dissociation Energies on Ether and Nonether Carbons of the Cyclic Ethers and Cyclic Ether Hydroperoxides. C−H bond dissociation enthalpies are reported from the calculated ΔH°f,298 of parent molecule and their radical corresponding to loss of hydrogen atoms, where the 3157



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Figure 5. Comparison of C―H bond dissociation enthalpies for yC2O-yC4O cyclic ethers versus cyclic alkanes (top). C−H BDEs secondary sites cyclic ethers versus cyclic alkanes with and without HOO group (lower left). C−H BDEs on ether carbons versus alkanes with and without HOO (lower right) (j = radical site, yCn, alkanes; yCnO, ethers; yCn-q, hydroperoxide alkane; yCn-q, hydroperoxide cyclic ether; Qc-eth, HOO on ether carbon; QC-sec, HOO on secondary carbon).

Table 9. Comparison of Peroxy Bond Dissociation Enthalpies (OO−H) for yC2O-yC4O Cyclic Ethersd

a

Reference 24. bReference 53. cGroup Additivity. dUnits: kcal mol−1.

bond dissociation enthalpies on corresponding cyclic alkanes, which suggests that nonether carbon sites in cyclic ethers are less reactive than the carbon sites in cyclic alkanes. Nonether carbon site C−H bond dissociation enthalpies of cyclic ethers without peroxy groups (group 1) are 0.8−2.1 kcal mol−1 lower versus cyclic ethers with the peroxy group in the ether position (group 3), and 1.7 kcal mol−1 lower versus cyclic ethers with the peroxy group in the nonether position (group 5). Nonether carbon site C−H bond dissociation enthalpies of

cyclic ethers with the peroxy group in the ether position (group 3) are similar (only ∼0.1−0.5 kcal mol−1 lower) to cyclic ethers with the peroxy group in the nonether position (group 5). The presence of the peroxy group in the ring (regardless of being on the ether carbon or nonether carbons) increases the C−H bond dissociation enthalpies. The nonether carbon site C−H bond dissociation enthalpy for the oxolane hydroperoxide, with the peroxy group on the ether carbon, is 0.8 kcal mol−1 higher 3158



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Figure 6. Comparison of OO−H (left) and O−OH (right) bond dissociation enthalpies for yC2O-yC4O cyclic ethers (j = radical site; see caption of Figure 5).

Table 10. Comparison of O−OH Bond Dissociation Enthalpies for yC3-yC5 Cyclic Alkanes and yC2O-yC4O Cyclic Ethersc

a)

Reference 24.

b)

Reference 47. cUnits: kcal mol−1.

6, left). The OO−H BDEs on cyclic ethers with the peroxy group bonded to ether carbon are 3.33 and 2.37 kcal mol−1 stronger (for oxetane and oxolane, respectively) versus cyclic ethers with the peroxy group bonded to the nonether carbon. The trend is similar to that of linear alkanes and ethers, where the OO−H bond dissociation enthalpies are ∼2.5 kcal mol−1 higher on ether carbons than on carbons of normal alkanes. The OO−H BDSs for cyclic alkanes are ∼1 kcal mol−1 lower than OO−H bonds on comparable ring size, nonether carbons of cyclic ethers. In all cases, the OO−H bond dissociation enthalpies decrease with increasing number of carbons in the ring (for ether carbons 90.4, 89.9, and 88.6 kcal mol−1 for y(cco)qeth•, y(ccco)qeth•, and y(cccco)qeth•, respectively, and for secondary carbons 86.56 and 86.26 kcal mol−1 for y(ccco)qsec• and y(cccco)qsec•, respectively), and for 5-member rings the bonds are similar to linear alkanes and ethers (85.1 kcal mol−1 for (CH3)2CHOO−H).53 RO−OH Bond Dissociation Energies. The O−OH bond dissociation enthalpies are reported from the calculated ΔfH°298 of parent hydroperoxide molecule corresponding to loss of • OH, formation of their alkoxy radical. The enthalpies of parent molecule alcohols and hydroperoxides and corresponding radicals are calculated in this study, with the value of 8.9554 kcal mol−1 for •OH at 298.15 K. Table 10 and Figure 6 compare the O−OH bond dissociation energies for cyclic alkanes and ethers (see Figure 6, right). O−OH bond dissociation enthalpies for cyclic ethers

when the radical site is adjacent to the carbon bonded to the peroxy group. C−H bond dissociation enthalpies on ether carbons of cyclic ethers without peroxy groups (group 2), are 2.9−3.4 kcal mol−1 lower versus cyclic ethers with the peroxy group in the ether position (group 4), and 1.0−1.2 kcal mol−1 higher versus cyclic ethers with the peroxy group in the nonether position (group 6). C−H bond dissociation enthalpies for ether carbons on cyclic ethers with the peroxy group in the ether position (group 4) are ∼3.9−4.5 kcal mol−1 higher versus cyclic ethers with the peroxy group in the nonether position (group 6). The presence of the peroxy group bonded to the nonether carbon in the ring decreases the C−H bond dissociation enthalpies, making the carbons in the ether positions more reactive. The ether carbon site C−H bond dissociation enthalpy for the oxolane hydroperoxide, with the peroxy group in the ether carbon, is 2.3 kcal mol−1 lower when the radical site is adjacent to the carbon bonded to the peroxy group. In all cases and as with comparable ring size cyclic alkanes, the C−H bond dissociation enthalpies decrease with increasing number of carbons in the ring, and for 5-member rings, the bonds are similar to linear alkanes and ethers (99.12 kcal mol−1 for CH3CH•CH351 and 95.01 kcal mol−1 for CH3CH•OCH352). Cyclic Ether ROO−H Bond Dissociation Energies. Table 9 summarizes and compares the OO−H peroxide bond dissociation enthalpies for cyclic ethers and alkanes (see Figure 3159



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Table 11. Comparison of R−OOH Bond Dissociation Enthalpies for yC3-yC5 Cyclic Alkanes and yC2O-yC4O Cyclic Ethersc

a

Reference 24. bReference 47. cUnits: kcal mol−1.

dissociation enthalpy for oxetane is 1.7 kcal mol−1 higher (73.7 kcal mol−1). Cyclic Ether Alcohol RO−H Bond Dissociation Energies. Table 12 and Figure 8 compare the O−H alkoxy bond dissociation enthalpies for the cyclic alkanes and ethers. The O−H bond dissociation enthalpy for oxetane with the alcohol group bonded to the nonether carbon is only 0.7 kcal mol−1 higher versus oxetane with the alcohol group bonded to the ether carbon. The RO−H bond is 1.8 kcal mol−1 higher for oxolane when the alcohol group is bonded to the ether carbon versus oxolane with the alcohol group bonded to the nonether carbon. In the 5-member ring, the OH group is closer to the ether oxygen than in the 4-member ring, hence causing the Oalcohol−H···Oether hydrogen bonding to be stronger in the 5member ring. The Halcohol−Oether ring distance is 2.45 Å for the 5-member ring, and the Halcohol−Oether distance is 2.64 Å for the 4-member ring; see Figure 9. The O−H bonds for cyclic alkanes and nonether carbons in the cyclic ethers are similar, with these ether carbons showing only ∼0.5 kcal mol−1 stronger O−H bond dissociation energies. The O−H bond dissociation enthalpies increase with decreasing ring strain (increasing number of carbons in ring) when the alcohol group is on the ether carbon (98.2, 104.3, and 108.0 kcal mol−1 for y(cco)oeth•, y(ccco)oeth•, and y(cccco)oeth•, respectively). Differently, the O−H bonds are similar for y(ccco)osec• and y(cccco)osec•, respectively, when the alcohol group is on the nonether carbons 105.0 and 104.7 kcal mol−1; and this is similar to the case of alkanes (105.1 kcal mol−1 for (CH3)2CHO•).53 R• + 3O2 Well-Depths. The R• + 3O2 well-depth is an important factor in kinetics for the chemical activation analysis for these association reactions, where intramolecular H transfers and HO2 molecular elimination barriers range from 42 to ∼12 kcal mol−1.39 The newly formed peroxy adduct in these reactions has sufficient energy to react over these barriers before stabilization. Table 13 summarizes the well-depths for each of the ether systems, and Figure 10 compares the R−OO well-depths for cyclic alkanes with ether and nonether carbons. The alkanes have several kcal mol−1 stronger R−OO bond dissociation energies than the nonether C−OO bonds and the ether C−OO are weaker for the respective 3- and 4-member ring systems. The alkyl and ether R−OO bonds for the 5-member ring systems are all similar. The well-depth is significant for the more highly strained systems and decreases significantly with loss of ring strain. R• + 3 O2 well-depths for the three cyclic yC•2O (oxirane), yC•3O (oxetane), and yC•4O (oxolane) are 40.5, 37.9/36.3 (qeth/qsec) and 37.1/34.9 (qeth/qsec) kcal mol−1, respectively. This trend is similar for the respective hydrocarbon rings, where the R• +

with the peroxy group bonded to the ether carbon are 0.7 and 1.7 kcal mol−1 stronger (for oxetane and oxolane, respectively) versus cyclic ethers with the peroxy group bonded to the nonether carbon. The O−OH bonds for cyclic alkanes are ∼1 kcal mol−1 lower compared to the bonds in the cyclic ethers with the peroxy group bonded to the nonether carbon. The O−OH bond dissociation enthalpies increase with increasing size of the ring (decreasing ring strain) when the alkoxy radical is on the ether carbon: 36.7, 45.1, and 47.9 kcal mol−1 for y(cco)qeth, y(ccco)qeth, and y(cccco)qeth, respectively. The O−OH bonds for oxetane and oxolane with the peroxy group in the nonether carbon are 44.4 and 46.2 kcal mol−1 for y(ccco)osec• and y(cccco)osec•, respectively; these are similar to those of linear alkanes (44.9 kcal mol−1 for (CH3)2CHO•).53 R−OOH Bond Dissociation Energies. Table 11 and Figure 7 compare the R−OOH bond dissociation enthalpies for the

Figure 7. Comparison of R−OOH bond dissociation enthalpies for yC2O-yC4O cyclic ethers (j = radical site; see caption of Figure 5).

cyclic alkanes and ethers. The bond dissociation enthalpy decreases with increasing ring size, and it is ∼4.5 kcal mol−1 higher for the cyclic ethers with the peroxy group bonded to the ether carbon versus the cyclic ether with the peroxy group bonded to the secondary carbon. Cyclic alkanes have very similar R−OOH BDEs compared to the cyclic ethers with the peroxy group in the secondary carbon. The bond dissociation enthalpy for oxolane with the peroxy group bonded to the secondary carbon (71.9 kcal mol−1) is similar to the one of linear alkanes (72.0 kcal mol−1), whereas the R−OOH bond 3160



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Table 12. Comparison of Alcohol RO−H Bond Dissociation Enthalpies for y(C2O)−OH to y(C4O)−OH Cyclic Ethersc

a

Reference 24. bReference 47. cUnits: kcal mol−1.

Table 13. R• + 3O2 (chemical activation) Well-Depths for Each of the Systems Studied + O2a well-depth system

cyclic ethers

cyclic alkanes

y(c co) + O2 y(c•cco) + O2 y(cc•co) + O2 y(c•ccco) + O2 y(cc•cco) + O2

40.46 37.91 36.35 37.08 34.85

42.33 38.87

•

a

35.08


Figure 8. O−H bond dissociation enthalpies for yC2O-yC4O cyclic ethers (j = radical site). The increased BDE of the O−H bond of oxolane is due to an increase in H-bonding between alcohol H and ether oxygen. yCn−OH, hydroxyl cyclic alkane, yCnO−OH, hydroxyl cyclic ether; c−c(oh)−c, alkoxy alkane; o−c(oj)−o, hydroxyl on ether carbon; c−c(oj)−c, alkoxy on secondary carbon.

Figure 10. Comparison of R• + O2 well-depths for yC2O-yC4O cyclic ethers (j = radical site).

systems. Lowest energy geometries, frequencies, rotation barriers and moments of inertia were used for the determination of the entropy and heat capacity, as well as the entropy and heat capacity values for each of the studied systems versus temperature and are summarized in the Supporting Information. Group Additivity. Thermodynamic properties of the studied species have been determined using group additivity. Group additivity with corrections for rings is a straightforward and reasonably accurate calculation method to estimate thermodynamic properties of hydrocarbons and oxygenated hydrocarbons;21,55,56 it is particularly useful for application to larger molecules and in codes or databases for the estimation of thermochemical properties in reaction mechanism generation.

Figure 9. Comparison of the Halcohol−Oring bond distance for the 4and 5-member rings.

O2 well-depths for yC•3, yC•4, and yC•5 are 42.3, 38.9, and 35.1 kcal mol−1, respectively. Figures 11−13 illustrate the well depths and the initial intramolecular H atom transfer reaction energy diagrams for the three studied systems. The heat of formation values are average of the CBS-QB3 and G3MP2B3 level methods used. Entropy and Heat Capacity. Entropy and heat capacity values are obtained from SMCPS and ROTATOR calculations as described above. Table 14 summarizes the entropy (S°, 298 K) and heat capacity (Cp(T)) values obtained for the studied 3

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radical site beta scission reactions. The ring-opening reactions for the 3 and 4 membered rings result in either carbonyl or olefin Π bonds along with relief of ring strain; these are all exothermic. Carbonyl bond formation shows significantly more exothermicity than the olefin Π bond formation. The 5membered radical ring-opening reactions have endothermicity from 1.5 to 21.5 kcal mol−1. Our initial studies on these ringopening reactions shows that they all have barriers to the ringopening.

■

SUMMARY Thermochemical properties, enthalpies of formation, entropy, S°(T) and heat capacity, Cp°(T), values, bond dissociation enthalpies, and R• + 3O2 well-depths are determined for 3- to 5member cyclic ethers yC2O-yC4O, the C-ether and Csecondary alkyl radicals, peroxy radicals, alkoxy radicals, hydroperoxyalkyl radicals on both ether and secondary carbon sites. The computed enthalpies of formation via isodesmic work reactions for the cyclic ether yC2O-yC4O systems show good agreement with the literature data available. Oxirane y(cco) has both carbons bonded to ether link, the C−H bond dissociation energy is 104.5 kcal mol−1, and the C− H bond on an ether carbon is more than 5 kcal mol−1 lower than the C−H bond on a corresponding alkane (cyclopropane). This is similar to the case with normal alkyl ethers versus n-alkanes. Adding a hydroperoxide group to oxirane decreases the C−H bond on the nonperoxide carbon slightly, ∼0.4 kcal mol−1. The ROO−H bond on the hydroperoxide is 5 kcal mol−1 stronger than that on a normal alkane hydroperoxide. The RO−OH bond is only 36.7 kcal mol−1, some 9 kcal mol−1 lower than a normal alkane RO−OH bond. The well-depth for addition of oxygen to the oxirane radical is 40.5 kcal mol−1. The R−OH bond for the y(C2O)−OH alcohol is 98.2 kcal mol−1, about 7 kcal mol−1 weaker than a normal alkane RO−H. Oxetane and oxolane can have the HO2 hydroperoxy group on an ether carbon y(cccco)qet or on a secondary carbon y(cccco)qsec. The enthalpy of both cyclic systems with the peroxide on a C-sec is 10 kcal mol−1 higher than when the HO2 is on a C-eth carbon. This shows a strong stabilizing interaction

Figure 11. Reaction energy diagram for alkyl oxirane + 3O2, at 298 K (barriers of H transfer reaction not illustrated).

A set of new and several revised groups have been developed in order to include them in codes used for group additivity calculations. Table 15 summarizes the groups that have been developed, and the Appendix summarizes the enthalpy, entropy and heat capacity for the species studied during this work, using the new groups. Benson stated that the ring correction derived from group additivity reflects the strain energy of the corresponding cyclic compound since group values are derived from open-chain, “unstrained” compounds.3,57 However, he also recognizes the difficulty in separating strain energy from resonance energy using group additivity for some ring compounds. Table 16 summarizes the ring strains for the cyclic ethers, and the ring strains for the cyclic alkanes are reported for comparison. The ring strain is 0.6−1.3 kcal mol−1 lower for the cyclic ethers, compared to the cyclic alkanes. Thermochemistry for Radical Unimolecular Dissociation (beta scission) Ring-Opening Reactions. Table 17 lists the thermochemistry for ring-opening reactions of the ring

Figure 12. Reaction energy diagram for alkyl oxetane + 3O2, at 298 K (barriers of H transfer reaction not illustrated). 3162



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Figure 13. Reaction energy diagram for alkyl oxolane + 3O2, at 298 K (barriers of H transfer reaction not illustrated).

Table 14. Entropy (S°, 298 K) and Heat Capacity (Cp(T)) for the Studied Systemsa S°

a

Cp

species

298 K

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

y(cco) y(c•co) y(cco)qeth y(cco)qeth• y(c•co)qeth y(cc•o)qeth y(ccco) y(c•cco) y(cc•co) y(ccco)qeth y(ccco)qeth• y(c•cco)qeth y(cc•co)qeth y(ccco)qsec y(ccco)qsec• y(c•cco)qsec y(cccco) y(c•ccco) y(cc•cco) y(cccco)qeth y(cccco)qeth• y(c•ccco)qeth y(cc•cco)qeth y(ccc•co)qeth y(cccco)qeth y(cccco)qeth• y(c•ccco)qeth y(ccc•co)qeth y(cccc•o)qeth

59.30 58.95 74.13 72.53 75.75 75.85 67.08 64.72 66.21 75.85 79.86 77.84 79.02 81.63 80.89 79.73 72.66 70.05 71.23 80.57 85.57 82.85 84.33 83.24 85.66 85.64 87.40 87.96 84.82

11.22 11.02 20.90 17.63 20.31 20.03 14.94 15.03 15.84 23.86 21.61 24.80 25.14 22.94 20.92 26.12 19.03 19.26 19.82 29.12 25.38 28.14 30.24 30.14 27.82 25.31 29.18 28.73 28.49

14.58 13.88 25.62 21.56 24.41 24.05 20.05 19.73 20.37 31.09 27.13 31.20 31.60 29.14 26.58 31.70 25.89 25.68 26.11 37.69 32.71 36.63 37.88 37.95 35.67 32.67 36.32 35.79 35.81

17.69 16.38 29.41 24.88 27.75 27.39 24.83 23.94 24.46 37.16 32.09 36.20 36.74 34.59 31.63 36.02 32.28 31.46 31.82 44.87 39.28 43.55 44.12 44.26 42.59 39.26 42.44 41.91 42.02

20.31 18.34 32.22 27.53 30.23 29.90 28.89 27.43 27.87 41.86 36.16 39.98 40.58 39.03 35.78 39.34 37.70 36.29 36.61 50.54 44.73 48.84 48.99 49.19 48.25 44.73 47.37 46.89 47.02

24.30 20.95 35.98 31.33 33.43 33.18 35.13 32.67 33.02 48.23 42.17 45.12 45.65 45.52 41.91 44.10 46.06 43.62 43.90 58.61 52.89 56.06 55.93 56.14 56.68 52.92 54.59 54.25 54.34

27.18 22.47 38.46 33.91 35.35 35.17 39.62 36.39 36.69 52.26 46.34 48.46 48.83 49.98 46.16 47.40 52.08 48.86 49.12 64.05 58.61 60.81 60.64 60.83 62.58 58.66 59.61 59.39 59.45

31.59 24.22 42.20 37.68 38.02 37.97 46.41 42.00 42.21 57.91 52.45 53.23 53.33 56.57 52.38 52.42 61.18 56.78 56.96 72.11 67.10 67.78 67.66 67.76 71.41 67.16 67.12 67.07 67.08

Units: S° (cal mol−1); Cp (cal mol−1 K−1).

carbon y(ccco)qsec, the ROO−H bond is weaker at 86.5 and the Ceth−H bond is also lower, 94.4 kcal mol−1, than when the HO2 group is on the other ether carbon. The enthalpy of oxetane with a hydroperoxide or alcohol group on the secondary carbon is 11 kcal mol−1 higher than that of the isomer when the hydroperoxide is on the ether carbon. There is significant stabilization between OH or HO2 groups and the ether, through the ether carbon. Oxolane 5-member ring also has the Ceth and Csec sites for an hydroperoxy or alcohol group bonding and also has Ceth−H

between the peroxide group and the ether oxygen through the C-et carbon. The Ceth−H bond dissociation energy and the ΔH°f,298 for the corresponding Ceth carbon radical of oxetane y(c•cco) are 5.5 kcal mol−1 lower than the C-sec bond and the ΔfHo(298) of the secondary CsecH carbon radical y(cc•co). Adding a hydroperoxide group to the oxetane ether carbon y(ccco)qet has the ROO−H bond on the peroxide group at 90.4, some 5 kcal mol−1 stronger than on a normal alkyl hydroperoxide. When the hydroperoxide is on the secondary (nonether) 3163



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Table 15. Groups Developed in This Study, and Previous Determined Groups Useda Cp°(T) group

ΔH°f,298b

S° (298)

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

ref

developed groups stable groups CY/C2O CY/C3O CY/C4O CY/C2O/Q CY/C3O/Qe CY/C3O/Qs CY/C4O/Qe CY/C4O/Qs radical groups CY/CJ2O CY/CJ2O/Qe CY/C2O/QeJ CY/C3JO-e CY/C3JO-s CY/CJ3O-e/Qe CY/CJ3O-s/Qe CY/CJ3O-e/Qs CY/C3O/QeJ CY/C3O/QsJ CY/C4JO-e CY/C4JO-s CY/CJ4O-e/Qe CY/CJ4O-s/Qe CY/CJ4O-s2/Qe CY/CJ4O-e2/Qs CY/CJ4O-s/Qs CY/CJ4O-e/Qs CY/C4O/QeJ CY/C4O/QsJ C/C2/H2 C/C2/H/O C/C/H2/O C/C/H/O2 O/C/O O/H/O O/C2 a

26.68 25.17 5.29 30.02 22.92 28.46 3.33 6.83

31.02 29.38 25.54 31.35 23.65 27.98 18.95 22.59

−2.16 −3.94 −5.35 −1.85 −4.39 −4.35 −4.63 −4.97

−2.82 −4.30 −5.41 −2.06 −3.54 −4.93 −3.89 −5.35

−2.61 −3.72 −4.52 −2.17 −2.67 −4.58 −3.21 −4.83

−2.35 −3.12 −3.66 −2.06 −1.77 −3.86 −2.44 −3.99

−2.32 −2.56 −2.70 −2.31 −1.13 −3.38 −1.82 −3.29

−2.08 −1.98 −1.86 −2.93 −1.47 −3.09 −2.02 −2.83

2.33 2.95 3.52 −0.01 1.50 1.57 1.50 2.21

104.51 104.33 90.41 95.43 101.71 98.30 103.78 94.42 89.89 86.56 93.74 98.27 96.99 99.10 99.85 92.49 100.03 94.78 88.63 86.26

−0.35 1.62 −1.60 −2.36 −0.87 1.99 3.17 −1.90 4.01 −0.74 −2.61 −1.43 2.28 3.76 2.67 1.74 2.30 −0.84 5.00 −0.02

−0.20 −0.59 −3.27 0.09 0.90 0.94 1.28 3.18 −2.25 −2.02 0.23 0.79 −0.98 1.12 1.02 1.36 0.91 0.67 −3.74 −2.51

−0.70 −1.31 −1.21 −1.66 −4.06 −4.53 −0.32 −0.89 0.32 −0.37 0.11 −0.96 0.51 −0.42 2.56 1.43 −3.96 −5.07 −2.56 −2.96 −0.21 −0.82 0.22 −0.46 −1.06 −1.32 0.19 −0.75 0.26 −0.61 0.65 −0.15 0.12 −0.68 0.14 −0.57 −4.98 −5.59 −3.00 −3.33 known groups

−1.97 −1.99 −4.69 −1.46 −1.02 −1.88 −1.28 0.31 −5.70 −3.25 −1.41 −1.09 −1.70 −1.55 −1.35 −0.88 −1.36 −1.23 −5.81 −3.52

−3.35 −2.55 −4.65 −2.46 −2.11 −3.11 −2.58 −1.42 −6.06 −3.61 −2.44 −2.16 −2.55 −2.68 −2.47 −2.09 −2.43 −2.34 −5.72 −3.76

−4.71 −3.11 −4.55 −3.23 −2.93 −3.80 −3.43 −2.58 −5.92 −3.82 −3.22 −2.96 −3.24 −3.41 −3.22 −2.97 −3.19 −3.13 −5.44 −3.92

−11.97 −4.18 −4.52 −4.41 −4.20 −4.68 −4.58 −4.15 −5.46 −4.19 −4.40 −4.22 −4.33 −4.45 −4.35 −4.29 −4.34 −4.33 −5.01 −4.25

−4.93 −7.20 −8.10 −16.00 −5.50 −16.30 −23.20

9.42 −11.00 9.80 −12.07 8.54 27.83 8.68

5.50 4.80 4.99 5.25 3.90 5.21 3.40

6.95 6.64 6.85 7.10 4.31 5.72 3.70

8.25 8.10 8.30 8.81 4.60 6.17 3.70

9.35 8.73 9.43 9.55 4.84 6.66 3.80

11.07 9.81 11.11 10.31 5.32 7.15 4.40

12.34 10.40 12.33 11.05 5.80 7.61 4.60

14.20 11.51 12.33 11.05 8.43 4.60

21 65 65 65 65 65 65

Units: kcal mol−1. bRepresents ΔH°f,298 for the stable groups, and bond dissociation enthalpy for the radical groups.

corresponding Csec−H BDE and y(cc•cc)q-sec formation enthalpy. A HO2 or OH group on the ether carbon is 10 kcal mol−1 lower in enthalpy than the corresponding C-sec isomer. Adding a hydroperoxide group to the oxetane ether carbon y(ccco)qeth has the ROO−H bond on the peroxide group at 88.6 kcal mol−1, some 2.5 kcal mol−1 stronger than on a normal alkyl hydroperoxide. The Ceth−H bond dissociation energy on the nonperoxide ether carbon is 97 kcal mol−1, some 2−3 kcal mol−1 lower than the 99.1 (Csec adjacent to peroxy ether carbon) and 99.9 kcal mol−1 (Csec adjacent to nonperoxide Ceth) on the two different CsecH carbons. Oxolane with a hydroperoxy group on a Csec (y(cccc)qsec) has a 10 kcal mol−1 higher enthalpy than when the peroxide is on the Ceth carbon y(cccc)qeth). The bond dissociation energies for y(c•ccco)qsec, y(cc•cco)qsec, and y(cccc•o)qsec are 92.5, 100.0, and 94.8 kcal mol−1,

Table 16. Ring Strains for Cyclic Alkanes and Ethers

and Csec−H bonds to evaluate. As with oxetane, the Ceth−H bond dissociation energies and the y(c•ccc)qeth radical formation energies are 4.5 kcal mol−1 lower than the 3164



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Table 17. Thermochemistry of Ring-Opening, Beta Scission Reactionsa

a

respectively. The ROO−H bond on y(cccc)qsec is 86.3 kcal mol−1, near that of normal hydrocarbons. R−OO Bond Dissociation Energies. The R• + 3O2 welldepths are about 2 kcal mol−1 lower for cyclic ethers than for cyclic alkanes, and well-depths decrease with decreasing ring strain for both cyclic alkanes and ethers. In all three ring systems, the C−H bond dissociation enthalpies decrease with increasing number of carbons in the ring, and for 5-member rings the bonds are similar to linear alkanes and ethers. The presence of the ether oxygen in the ring stabilizes the cyclic hydroperoxides (OO−H bonds get stronger), especially when the peroxy group is bonded to the ether carbon.

ASSOCIATED CONTENT

S Supporting Information *

Calculated reaction enthalpies at 298 K, ideal gas-phase thermodynamic properties versus temperature, the vibration frequencies of the studied species, the geometric parameters of the studied species, the work reactions used for the studied species, a detailed description of the determination of the uncertainties, and the groups included for the determination of the thermochemistry of the studied species by Group Additivity. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge STTR funding from the U.S. Navy (Contract Number 68335-09-C-0376), and the Basque Government for partial funding. 3165



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